Question: Simplify the following expression: $ p = \dfrac{-2}{5} - \dfrac{z + 5}{9} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-2}{5} \times \dfrac{9}{9} = \dfrac{-18}{45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{z + 5}{9} \times \dfrac{5}{5} = \dfrac{5z + 25}{45} $ Therefore $ p = \dfrac{-18}{45} - \dfrac{5z + 25}{45} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-18 - (5z + 25) }{45} $ Distribute the negative sign: $p = \dfrac{-18 - 5z - 25}{45}$ $p = \dfrac{-5z - 43}{45}$